Search results for: Bees Algorithm (BA); Approximate Solutions; Blasius Differential Equation.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 6064

Search results for: Bees Algorithm (BA); Approximate Solutions; Blasius Differential Equation.

5284 An Improved Conjugate Gradient Based Learning Algorithm for Back Propagation Neural Networks

Authors: N. M. Nawi, R. S. Ransing, M. R. Ransing

Abstract:

The conjugate gradient optimization algorithm is combined with the modified back propagation algorithm to yield a computationally efficient algorithm for training multilayer perceptron (MLP) networks (CGFR/AG). The computational efficiency is enhanced by adaptively modifying initial search direction as described in the following steps: (1) Modification on standard back propagation algorithm by introducing a gain variation term in the activation function, (2) Calculation of the gradient descent of error with respect to the weights and gains values and (3) the determination of a new search direction by using information calculated in step (2). The performance of the proposed method is demonstrated by comparing accuracy and computation time with the conjugate gradient algorithm used in MATLAB neural network toolbox. The results show that the computational efficiency of the proposed method was better than the standard conjugate gradient algorithm.

Keywords: Adaptive gain variation, back-propagation, activation function, conjugate gradient, search direction.

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5283 Target Signal Detection Using MUSIC Spectrum in Noise Environment

Authors: Sangjun Park, Sangbae Jeong, Moonsung Han, Minsoo hahn

Abstract:

In this paper, a target signal detection method using multiple signal classification (MUSIC) algorithm is proposed. The MUSIC algorithm is a subspace-based direction of arrival (DOA) estimation method. The algorithm detects the DOAs of multiple sources using the inverse of the eigenvalue-weighted eigen spectra. To apply the algorithm to target signal detection for GSC-based beamforming, we utilize its spectral response for the target DOA in noisy conditions. For evaluation of the algorithm, the performance of the proposed target signal detection method is compared with that of the normalized cross-correlation (NCC), the fixed beamforming, and the power ratio method. Experimental results show that the proposed algorithm significantly outperforms the conventional ones in receiver operating characteristics(ROC) curves.

Keywords: Beamforming, direction of arrival, multiple signal classification, target signal detection.

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5282 An Estimation of the Performance of HRLS Algorithm

Authors: Shazia Javed, Noor Atinah Ahmad

Abstract:

The householder RLS (HRLS) algorithm is an O(N2) algorithm which recursively updates an arbitrary square-root of the input data correlation matrix and naturally provides the LS weight vector. A data dependent householder matrix is applied for such an update. In this paper a recursive estimate of the eigenvalue spread and misalignment of the algorithm is presented at a very low computational cost. Misalignment is found to be highly sensitive to the eigenvalue spread of input signals, output noise of the system and exponential window. Simulation results show noticeable degradation in the misalignment by increase in eigenvalue spread as well as system-s output noise, while exponential window was kept constant.

Keywords: HRLS algorithm, eigenvalue spread, misalignment.

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5281 A Quantum Algorithm of Constructing Image Histogram

Authors: Yi Zhang, Kai Lu, Ying-hui Gao, Mo Wang

Abstract:

Histogram plays an important statistical role in digital image processing. However, the existing quantum image models are deficient to do this kind of image statistical processing because different gray scales are not distinguishable. In this paper, a novel quantum image representation model is proposed firstly in which the pixels with different gray scales can be distinguished and operated simultaneously. Based on the new model, a fast quantum algorithm of constructing histogram for quantum image is designed. Performance comparison reveals that the new quantum algorithm could achieve an approximately quadratic speedup than the classical counterpart. The proposed quantum model and algorithm have significant meanings for the future researches of quantum image processing.

Keywords: Quantum Image Representation, Quantum Algorithm, Image Histogram.

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5280 Optimal Capacitor Allocation for loss reduction in Distribution System Using Fuzzy and Plant Growth Simulation Algorithm

Authors: R. Srinivasa Rao

Abstract:

This paper presents a new and efficient approach for capacitor placement in radial distribution systems that determine the optimal locations and size of capacitor with an objective of improving the voltage profile and reduction of power loss. The solution methodology has two parts: in part one the loss sensitivity factors are used to select the candidate locations for the capacitor placement and in part two a new algorithm that employs Plant growth Simulation Algorithm (PGSA) is used to estimate the optimal size of capacitors at the optimal buses determined in part one. The main advantage of the proposed method is that it does not require any external control parameters. The other advantage is that it handles the objective function and the constraints separately, avoiding the trouble to determine the barrier factors. The proposed method is applied to 9 and 34 bus radial distribution systems. The solutions obtained by the proposed method are compared with other methods. The proposed method has outperformed the other methods in terms of the quality of solution.

Keywords: Distribution systems, Capacitor allocation, Loss reduction, Fuzzy, PGSA.

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5279 A Fault Tolerant Token-based Algorithm for Group Mutual Exclusion in Distributed Systems

Authors: Abhishek Swaroop, Awadhesh Kumar Singh

Abstract:

The group mutual exclusion (GME) problem is a variant of the mutual exclusion problem. In the present paper a token-based group mutual exclusion algorithm, capable of handling transient faults, is proposed. The algorithm uses the concept of dynamic request sets. A time out mechanism is used to detect the token loss; also, a distributed scheme is used to regenerate the token. The worst case message complexity of the algorithm is n+1. The maximum concurrency and forum switch complexity of the algorithm are n and min (n, m) respectively, where n is the number of processes and m is the number of groups. The algorithm also satisfies another desirable property called smooth admission. The scheme can also be adapted to handle the extended group mutual exclusion problem.

Keywords: Dynamic request sets, Fault tolerance, Smoothadmission, Transient faults.

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5278 A Hybrid Differential Transform Approach for Laser Heating of a Double-Layered Thin Film

Authors: Cheng-Ying Lo

Abstract:

This paper adopted the hybrid differential transform approach for studying heat transfer problems in a gold/chromium thin film with an ultra-short-pulsed laser beam projecting on the gold side. The physical system, formulated based on the hyperbolic two-step heat transfer model, covers three characteristics: (i) coupling effects between the electron/lattice systems, (ii) thermal wave propagation in metals, and (iii) radiation effects along the interface. The differential transform method is used to transfer the governing equations in the time domain into the spectrum equations, which is further discretized in the space domain by the finite difference method. The results, obtained through a recursive process, show that the electron temperature in the gold film can rise up to several thousand degrees before its electron/lattice systems reach equilibrium at only several hundred degrees. The electron and lattice temperatures in the chromium film are much lower than those in the gold film.

Keywords: Differential transform, hyperbolic heat transfer, thin film, ultrashort-pulsed laser.

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5277 Positive Periodic Solutions for a Neutral Impulsive Delay Competition System

Authors: Daiming Wang

Abstract:

In this paper, a neutral impulsive competition system with distributed delays is studied by using Mawhin-s coincidence degree theory and the mean value theorem of differential calculus. Sufficient conditions on the existence of positive periodic solution of the system are obtained.

Keywords: Neutral impulsive delay system, competitive system, coincidence degree, periodic solution, existence.

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5276 Optimal Capacitor Placement in a Radial Distribution System using Plant Growth Simulation Algorithm

Authors: R. Srinivasa Rao, S. V. L. Narasimham

Abstract:

This paper presents a new and efficient approach for capacitor placement in radial distribution systems that determine the optimal locations and size of capacitor with an objective of improving the voltage profile and reduction of power loss. The solution methodology has two parts: in part one the loss sensitivity factors are used to select the candidate locations for the capacitor placement and in part two a new algorithm that employs Plant growth Simulation Algorithm (PGSA) is used to estimate the optimal size of capacitors at the optimal buses determined in part one. The main advantage of the proposed method is that it does not require any external control parameters. The other advantage is that it handles the objective function and the constraints separately, avoiding the trouble to determine the barrier factors. The proposed method is applied to 9, 34, and 85-bus radial distribution systems. The solutions obtained by the proposed method are compared with other methods. The proposed method has outperformed the other methods in terms of the quality of solution.

Keywords: Distribution systems, Capacitor placement, loss reduction, Loss sensitivity factors, PGSA.

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5275 An Authentic Algorithm for Ciphering and Deciphering Called Latin Djokovic

Authors: Diogen Babuc

Abstract:

The question that is a motivation of writing is how many devote themselves to discovering something in the world of science where much is discerned and revealed, but at the same time, much is unknown. The insightful elements of this algorithm are the ciphering and deciphering algorithms of Playfair, Caesar, and Vigen`ere. Only a few of their main properties are taken and modified, with the aim of forming a specific functionality of the algorithm called Latin Djokovic. Specifically, a string is entered as input data. A key k is given, with a random value between the values a and b = a+3. The obtained value is stored in a variable with the aim of being constant during the run of the algorithm. In correlation to the given key, the string is divided into several groups of substrings, and each substring has a length of k characters. The next step involves encoding each substring from the list of existing substrings. Encoding is performed using the basis of Caesar algorithm, i.e. shifting with k characters. However, that k is incremented by 1 when moving to the next substring in that list. When the value of k becomes greater than b + 1, it will return to its initial value. The algorithm is executed, following the same procedure, until the last substring in the list is traversed. Using this polyalphabetic method, ciphering and deciphering of strings are achieved. The algorithm also works for a 100-character string. The x character is not used when the number of characters in a substring is incompatible with the expected length. The algorithm is simple to implement, but it is questionable if it works better than the other methods, from the point of view of execution time and storage space.

Keywords: Ciphering and deciphering, Authentic Algorithm, Polyalphabetic Cipher, Random Key, methods comparison.

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5274 Modes of Collapse of Compress–Expand Member under Axial Loading

Authors: Shigeyuki Haruyama, Aidil Khaidir Bin Muhamad, Ken Kaminishi, Dai-Heng Chen

Abstract:

In this paper, a study on the modes of collapse of compress- expand members are presented. Compress- expand member is a compact, multiple-combined cylinders, to be proposed as energy absorbers. Previous studies on the compress- expand member have clarified its energy absorption efficiency, proposed an approximate equation to describe its deformation characteristics and also highlighted the improvement that it has brought. However, for the member to be practical, the actual range of geometrical dimension that it can maintain its applicability must be investigated. In this study, using a virtualized materials that comply the bilinear hardening law, Finite element Method (FEM) analysis on the collapse modes of compress- expand member have been conducted. Deformation maps that plotted the member's collapse modes with regards to the member's geometric and material parameters were then presented in order to determine the dimensional range of each collapse modes.

Keywords: Axial collapse, compress-expand member, tubular member, finite element method, modes of collapse, thin-walled cylindrical tube.

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5273 An Energy Efficient Algorithm for Distributed Mutual Exclusion in Mobile Ad-hoc Networks

Authors: Sayani Sil, Sukanta Das

Abstract:

This paper reports a distributed mutual exclusion algorithm for mobile Ad-hoc networks. The network is clustered hierarchically. The proposed algorithm considers the clustered network as a logical tree and develops a token passing scheme to get the mutual exclusion. The performance analysis and simulation results show that its message requirement is optimal, and thus the algorithm is energy efficient.

Keywords: Critical section, Distributed mutual exclusion, MobileAd-hoc network, Token-based algorithms.

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5272 Enhanced Shell Sorting Algorithm

Authors: Basit Shahzad, Muhammad Tanvir Afzal

Abstract:

Many algorithms are available for sorting the unordered elements. Most important of them are Bubble sort, Heap sort, Insertion sort and Shell sort. These algorithms have their own pros and cons. Shell Sort which is an enhanced version of insertion sort, reduces the number of swaps of the elements being sorted to minimize the complexity and time as compared to insertion sort. Shell sort improves the efficiency of insertion sort by quickly shifting values to their destination. Average sort time is O(n1.25), while worst-case time is O(n1.5). It performs certain iterations. In each iteration it swaps some elements of the array in such a way that in last iteration when the value of h is one, the number of swaps will be reduced. Donald L. Shell invented a formula to calculate the value of ?h?. this work focuses to identify some improvement in the conventional Shell sort algorithm. ''Enhanced Shell Sort algorithm'' is an improvement in the algorithm to calculate the value of 'h'. It has been observed that by applying this algorithm, number of swaps can be reduced up to 60 percent as compared to the existing algorithm. In some other cases this enhancement was found faster than the existing algorithms available.

Keywords: Algorithm, Computation, Shell, Sorting.

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5271 Nonlinear Power Measurement Algorithm of the Input Mix Components of the Noise Signal and Pulse Interference

Authors: Alexey V. Klyuev, Valery P. Samarin, Viktor F. Klyuev, Andrey V. Klyuev

Abstract:

A power measurement algorithm of the input mix components of the noise signal and pulse interference is considered. The algorithm efficiency analysis has been carried out for different interference-to-signal ratio. Algorithm performance features have been explored by numerical experiment results.

Keywords: Noise signal, pulse interference, signal power, spectrum width, detection.

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5270 Performance Comparison and Evaluation of AdaBoost and SoftBoost Algorithms on Generic Object Recognition

Authors: Doaa Hegazy, Joachim Denzler

Abstract:

SoftBoost is a recently presented boosting algorithm, which trades off the size of achieved classification margin and generalization performance. This paper presents a performance evaluation of SoftBoost algorithm on the generic object recognition problem. An appearance-based generic object recognition model is used. The evaluation experiments are performed using a difficult object recognition benchmark. An assessment with respect to different degrees of label noise as well as a comparison to the well known AdaBoost algorithm is performed. The obtained results reveal that SoftBoost is encouraged to be used in cases when the training data is known to have a high degree of noise. Otherwise, using Adaboost can achieve better performance.

Keywords: SoftBoost algorithm, AdaBoost algorithm, Generic object recognition.

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5269 Image Segmentation Using the K-means Algorithm for Texture Features

Authors: Wan-Ting Lin, Chuen-Horng Lin, Tsung-Ho Wu, Yung-Kuan Chan

Abstract:

This study aims to segment objects using the K-means algorithm for texture features. Firstly, the algorithm transforms color images into gray images. This paper describes a novel technique for the extraction of texture features in an image. Then, in a group of similar features, objects and backgrounds are differentiated by using the K-means algorithm. Finally, this paper proposes a new object segmentation algorithm using the morphological technique. The experiments described include the segmentation of single and multiple objects featured in this paper. The region of an object can be accurately segmented out. The results can help to perform image retrieval and analyze features of an object, as are shown in this paper.

Keywords: k-mean, multiple objects, segmentation, texturefeatures.

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5268 An Attribute-Centre Based Decision Tree Classification Algorithm

Authors: Gökhan Silahtaroğlu

Abstract:

Decision tree algorithms have very important place at classification model of data mining. In literature, algorithms use entropy concept or gini index to form the tree. The shape of the classes and their closeness to each other some of the factors that affect the performance of the algorithm. In this paper we introduce a new decision tree algorithm which employs data (attribute) folding method and variation of the class variables over the branches to be created. A comparative performance analysis has been held between the proposed algorithm and C4.5.

Keywords: Classification, decision tree, split, pruning, entropy, gini.

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5267 Generational PipeLined Genetic Algorithm (PLGA)using Stochastic Selection

Authors: Malay K. Pakhira, Rajat K. De

Abstract:

In this paper, a pipelined version of genetic algorithm, called PLGA, and a corresponding hardware platform are described. The basic operations of conventional GA (CGA) are made pipelined using an appropriate selection scheme. The selection operator, used here, is stochastic in nature and is called SA-selection. This helps maintaining the basic generational nature of the proposed pipelined GA (PLGA). A number of benchmark problems are used to compare the performances of conventional roulette-wheel selection and the SA-selection. These include unimodal and multimodal functions with dimensionality varying from very small to very large. It is seen that the SA-selection scheme is giving comparable performances with respect to the classical roulette-wheel selection scheme, for all the instances, when quality of solutions and rate of convergence are considered. The speedups obtained by PLGA for different benchmarks are found to be significant. It is shown that a complete hardware pipeline can be developed using the proposed scheme, if parallel evaluation of the fitness expression is possible. In this connection a low-cost but very fast hardware evaluation unit is described. Results of simulation experiments show that in a pipelined hardware environment, PLGA will be much faster than CGA. In terms of efficiency, PLGA is found to outperform parallel GA (PGA) also.

Keywords: Hardware evaluation, Hardware pipeline, Optimization, Pipelined genetic algorithm, SA-selection.

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5266 Restartings: A Technique to Improve Classic Genetic Algorithms Performance

Authors: Grigorios N. Beligiannis, Georgios A. Tsirogiannis, Panayotis E. Pintelas

Abstract:

In this contribution, a way to enhance the performance of the classic Genetic Algorithm is proposed. The idea of restarting a Genetic Algorithm is applied in order to obtain better knowledge of the solution space of the problem. A new operator of 'insertion' is introduced so as to exploit (utilize) the information that has already been collected before the restarting procedure. Finally, numerical experiments comparing the performance of the classic Genetic Algorithm and the Genetic Algorithm with restartings, for some well known test functions, are given.

Keywords: Genetic Algorithms, Restartings, Search space exploration, Search space exploitation.

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5265 Reduce the Complexity of Material Requirement Planning on Excel by an Algorithm

Authors: Sumitra Nuanmeesri, Kanate Ploydanai

Abstract:

Many companies have excel, it is economy and well perform to use in material requirement planning (MRP) on excel. For several products, it, however, is complex problem to link the relationship between the tables of products because the relationship depends on bill of material (BOM). This paper presents algorithm to create MRP on excel, and links relationship between tables. The study reveals MRP that is created by the algorithm which is easier and faster than MRP that created by human. By this technique, MRP on excel might be good ways to improve a productivity of companies.

Keywords: Material requirement planning, Algorithm, Spreadsheet.

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5264 Combination Scheme of Affine Projection Algorithm Filters with Complementary Order

Authors: Young-Seok Choi

Abstract:

This paper proposes a complementary combination scheme of affine projection algorithm (APA) filters with different order of input regressors. A convex combination provides an interesting way to keep the advantage of APA having different order of input regressors. Consequently, a novel APA which has the rapid convergence and the reduced steady-state error is derived. Experimental results show the good properties of the proposed algorithm.

Keywords: Adaptive filter, affine projection algorithm, convex combination, input order.

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5263 Local Algorithm for Establishing a Virtual Backbone in 3D Ad Hoc Network

Authors: Alaa E. Abdallah, M. Bsoul, Emad E. Abdallah, Ahmad Al-Khasawneh, Muath Alzghool

Abstract:

Due to the limited lifetime of the nodes in ad hoc and sensor networks, energy efficiency needs to be an important design consideration in any routing algorithm. It is known that by employing a virtual backbone in a wireless network, the efficiency of any routing scheme for the network can be improved. One common design for routing protocols in mobile ad hoc networks is to use positioning information; we use the node-s geometric locations to introduce an algorithm that can construct the virtual backbone structure locally in 3D environment. The algorithm construction has a constant time.

Keywords: Virtual backbone, dominating set, UDG.

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5262 Study of Natural Convection Heat Transfer of Plate-Fin Heat Sink in a Closed Enclosure

Authors: Han-Taw Chen, Tzu-Hsiang Lin, Chung-Hou Lai

Abstract:

The present study applies the inverse method and three-dimensional CFD commercial software in conjunction with the experimental temperature data to investigate the heat transfer and fluid flow characteristics of the plate-fin heat sink in a rectangular closed enclosure. The inverse method with the finite difference method and the experimental temperature data is applied to determine the approximate heat transfer coefficient. Later, based on the obtained results, the zero-equation turbulence model is used to obtain the heat transfer and fluid flow characteristics between two fins. T0 validate the accuracy of the results obtained, the comparison of the heat transfer coefficient is made. The obtained temperature at selected measurement locations of the fin is also compared with experimental data. The effect of the height of the rectangular enclosure on the obtained results is discussed.

Keywords: Inverse method, FLUENT, Plate-fin heat sink, Heat transfer characteristics.

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5261 Combined DWT-CT Blind Digital Image Watermarking Algorithm

Authors: Nidal F. Shilbayeh, Belal AbuHaija, Zainab N. Al-Qudsy

Abstract:

In this paper, we propose a new robust and secure system that is based on the combination between two different transforms Discrete wavelet Transform (DWT) and Contourlet Transform (CT). The combined transforms will compensate the drawback of using each transform separately. The proposed algorithm has been designed, implemented and tested successfully. The experimental results showed that selecting the best sub-band for embedding from both transforms will improve the imperceptibility and robustness of the new combined algorithm. The evaluated imperceptibility of the combined DWT-CT algorithm which gave a PSNR value 88.11 and the combination DWT-CT algorithm improves robustness since it produced better robust against Gaussian noise attack. In addition to that, the implemented system shored a successful extraction method to extract watermark efficiently.

Keywords: DWT, CT, Digital Image Watermarking, Copyright Protection.

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5260 Stability Analysis in a Fractional Order Delayed Predator-Prey Model

Authors: Changjin Xu, Peiluan Li

Abstract:

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given to show the effectiveness of the approach presented in this paper.

Keywords: Fractional predator-prey model, laplace transform, characteristic equation.

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5259 An Implementation of MacMahon's Partition Analysis in Ordering the Lower Bound of Processing Elements for the Algorithm of LU Decomposition

Authors: Halil Snopce, Ilir Spahiu, Lavdrim Elmazi

Abstract:

A lot of Scientific and Engineering problems require the solution of large systems of linear equations of the form bAx in an effective manner. LU-Decomposition offers good choices for solving this problem. Our approach is to find the lower bound of processing elements needed for this purpose. Here is used the so called Omega calculus, as a computational method for solving problems via their corresponding Diophantine relation. From the corresponding algorithm is formed a system of linear diophantine equalities using the domain of computation which is given by the set of lattice points inside the polyhedron. Then is run the Mathematica program DiophantineGF.m. This program calculates the generating function from which is possible to find the number of solutions to the system of Diophantine equalities, which in fact gives the lower bound for the number of processors needed for the corresponding algorithm. There is given a mathematical explanation of the problem as well. Keywordsgenerating function, lattice points in polyhedron, lower bound of processor elements, system of Diophantine equationsand : calculus.

Keywords: generating function, lattice points in polyhedron, lower bound of processor elements, system of Diophantine equations and calculus.

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5258 Application of Fractional Model Predictive Control to Thermal System

Authors: Aymen Rhouma, Khaled Hcheichi, Sami Hafsi

Abstract:

The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller.

Keywords: Fractional model predictive control, fractional order systems, thermal system.

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5257 A Modified Inexact Uzawa Algorithm for Generalized Saddle Point Problems

Authors: Shu-Xin Miao

Abstract:

In this note, we discuss the convergence behavior of a modified inexact Uzawa algorithm for solving generalized saddle point problems, which is an extension of the result obtained in a recent paper [Z.H. Cao, Fast Uzawa algorithm for generalized saddle point problems, Appl. Numer. Math., 46 (2003) 157-171].

Keywords: Saddle point problem, inexact Uzawa algorithm, convergence behavior.

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5256 Role of Ionic Solutions Affect Water Treeing Propagation in XLPE Insulation for High Voltage Cable

Authors: T. Boonraksa, B. Marungsri

Abstract:

This paper presents the experimental results on role of ionic solutions affect water treeing propagation in cross-linked polyethylene insulation for high voltage cable. To study the water treeing expansion due to the ionic solutions, discs of 4mm thickness and 4cm diameter were taken from 115 kV XLPE insulation cable and were used as test specimen in this study. Ionic solutions composed of CuSO4, FeSO4, Na2SO4 and K2SO4 were used. Each specimen was immersed in 0.1 mole ionic solutions and was tested for 120 hrs. under a voltage stress at 7 kV AC rms, 1000 Hz. The results show that Na2SO4 and CuSO4solutions play an important role in the expansion of water treeing and cause degradation of the crosslinked polyethylene (XLPE) in the presence of the applied electric field.

Keywords: Ionic Solutions, Water Treeing, Water treeing Expansion, Cross-linked Polyethylene (XLPE).

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5255 Analysis of Permanence and Extinction of Enterprise Cluster Based On Ecology Theory

Authors: Ping Liu, Yongkun Li

Abstract:

This paper is concerned with the permanence and extinction problem of enterprises cluster constituted by m satellite enterprises and a dominant enterprise. We present the model involving impulsive effect based on ecology theory, which effectively describe the competition and cooperation of enterprises cluster in real economic environment. Applying comparison theorem of impulsive differential equation, we establish sufficient conditions which ultimately affect the fate of enterprises: permanence, extinction, and co-existence. Finally, we present numerical examples to explain the economical significance of mathematical results.

Keywords: Enterprise cluster, permanence, extinction, impulsive, comparison theorem.

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